Exercise 4 Page P28

Considering the scenarios of the given data sets, let's first determine the type of data it is. Then we can analyze the range, standard deviation, and variance for both sets.

Type of Data Set

If a given data set is population data, the desired statistic is known for every member of the given group. If a given data set is sample data, the desired statistic is known for a small, representative portion of the given group.

In this case we have been given the recorded wait times for two rides. We can assume that this data comes from a public transportation service that continually makes rides A and B. Therefore, the data set is sample data.

Analyzing the Data

To calculate the different statistical measures using a graphing calculator, we have to enter the data into lists. Do this by pressing the STAT button, selecting Edit, and then entering the values into the first two lists.

Once the data has been entered, push STAT once more. Under CALC, press ENTER once to select 1-Var Stats and a second time to see statistical information about the first list, L1.

Take note of the output on the resulting screen. To determine the range, look at the minimum and maximum values of the data set. Remember, variance is the square of the standard deviation. minX:& 11 maxX:& 60 Range:& 60-11=49 σ x:& 13.89 (σ x)^2:& 13.89^2≈ 192.93 Let's repeat this process for the second list, L2. Once more, press STAT and select 1-Var Stats with ENTER. Before pressing ENTER again, push 2nd and 2 to select L2.

Again, we can find all of the necessary information in the output. minX:& 31 maxX:& 50 Range:& 50-31=19 σ x:& 6.22 (σ x)^2:& 6.22^2≈ 38.69

Comparing the Data Sets

Now that we have found all of the necessary pieces of information from both of the data sets, we can compare the results. The standard deviation for Ride A is 210.54 and 42.25 for Ride B. Therefore, there is more variability in the sample times for Ride A.